We can model covalent bonding in molecules in essentially two ways:

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1 CHEM 2060 Lecture 22: VB Theory L22-1 PART FIVE: The Covalent Bond We can model covalent bonding in molecules in essentially two ways: 1. Localized Bonds (retains electron pair concept of Lewis Structures) Valence Bond (VB) model Hybridization of atomic orbitals (e.g., sp 3 hybridization) Advantages: Concept of bond order applies (single, double, triple bonds, etc.) Can discuss a bond and ignore the rest of the molecule Disadvantages: Hard to describe the properties of some species (e.g., O 2 ) 2. Delocalized Molecular Orbitals. Molecular Orbital (MO) model Advantages: Easily describes spectroscopic properties of most species. Disadvantages: Can be unnecessarily cumbersome.

2 CHEM 2060 Lecture 22: VB Theory L22-2 Valence Bond Theory H 2 as an example In order to describe the bonding in H 2, we use the atomic orbitals of the H atoms and mix them. H a + H b H 2 use the 1s orbitals of atoms H a and H b Combine wavefunction of 1s a and 1s b First guess: Multiply the functions. ψ I = 1s a (1) 1s b (2) This puts electron 1 in the 1s orbital of H a and electron 2 in the 1s orbital of H b. This is a lousy guess because it doesn t take into account that we will not be able to distinguish electrons 1 and 2 at short internuclear distances! Better is: ψ II (+) = 1s a (1) 1s b (2) + 1s a (2) 1s b (1) ψ II (-) = 1s a (1) 1s b (2) - 1s a (2) 1s b (1)

3 CHEM 2060 Lecture 22: VB Theory L22-3 curves: a) ψ I first guess (above) b) ψ II (+) bonding combination c) using Z* = 1.17 d) hybridize s orbital with 1% p e) include ionic contributions f) experimental energy g) ψ II (-) antibonding combo. Further improvements can be made. ψ(1s) = 1 $ Z & π % a 0 ' ) ( 3 Zr 2 e a 0 Change Z in atomic hydrogen wavefunction. There are 2 nuclei in the H 2 atom, Z* > Z. Can lower the curve the most using Z* = 1.17 (i.e., fits experimental curve best with 1.17)

4 CHEM 2060 Lecture 22: VB Theory L22-4 Better Guess: Invoke Hybridization Mixing atomic orbitals of the same atom is called HYBRIDIZATION. This is quite reasonable. After all the orbitals are only wavefunctions. Example: sp hybrid atomic orbitals are created from one s plus one p orbital RULE: Mix n AOs Get n HAOs Mix an s orbital and a p orbital Get 2 sp orbitals

5 CHEM 2060 Lecture 22: VB Theory L22-5 Why invoke hybridization for H 2? Conceptually, it seems unlikely that the 1s orbital should be able to mix with the 2p orbital because they are very far apart in energy. This is a bone of contention between the VB advocates and MO advocates! NEVERTHELESS, hybridization gives a lower energy. We know the real measured energy, so this is clearly nearer the truth. AND the bond is represented more accurately. Each H atom ought to distort the electron cloud on the other. Since 1s is spherically symmetric this does not represent the bond very well. 2p z orbital is not spherically symmetric, so we can add in a bit of this to make the bond look better (more overlap, better bonding).

6 CHEM 2060 Lecture 22: VB Theory L22-6 Wavefunctions now are: φ a = N(1s a + γz a ) φ b = N(1s b + γz b ) N = Normalization constant to make sure φ 2 =1 γ is the amount of 2p z orbital that is mixed with the 1s orbital on each atom Best fit is for only 1% contribution from 2p z. But 1% p-character improves wavefunction stability by 5%

7 CHEM 2060 Lecture 22: VB Theory L22-7 Ionic contribution Hybridization has improved the wavefunction stability, but the wavefunction from hybridization alone is still not a very good curve. It is not that close to the experimental value. Further improvements can be obtained by adding terms to the wavefunction where both electrons are on one atom (i.e., charge separation) Think of the Lewis dot resonance contributors: We do this by adding a weighting factor λ i.e. ψ = φ a (1) φ b (2) + φ a (2) φ b (1) + λφ a (1) φ a (2) + λφ b (1) φ b (2) For H 2, the best value for λ 0.25 λ 2 ~ 0.06, contribution is about 6% The resulting improvement in wavefunction stability is only 2-3%.

8 CHEM 2060 Lecture 22: VB Theory L22-8 VB theory and Quantum Mechanics In quantum mechanics, we use a trial wavefunction and improve it to better fit the experimental values (e.g., bond energies, orbital energies, distances, etc.) Better wavefunction = closer to experimental (minimum energy) Valence bond theory is one quantum mechanical approach and it uses hybridized atomic orbitals (hao s) to improve the wavefunctions such that they are a closer fit to experimental values. For the H 2 molecule, a 50-term wavefunction reproduces the experimental bond energy to within of the experimental. Obviously, this is done computationally. You will see this in CHEM You will also learn that some approaches give very good energies and very poor distances, and vice versa. This is a huge field of theoretical research, limited only by processor speed.